The Football Association has confirmed that the Argentina striker will not be charged retrospectively for the incident in Sunday's FA Cup semi-final at Wembley.
It follows confirmation that referee Chris Foy had at least seen part of the incident and acted on it during the match - Chelsea were awarded a free-kick.
Both of Aguero's boots made contact with the upper part of Luiz's left leg but under current FA rules only off-the-ball incidents or those viewed as "exceptional" - which would, for example, warrant more than a three-match ban - are dealt with retrospectively.
There was an outcry when the FA took a similar view on Wigan's Callum McManaman after his studs-up challenge on Newcastle's Massadio Haidara, who was carried from the field on a stretcher, last month.
This was slightly different in that, unlike Haidara, Luiz suffered no serious harm and played on until the end of the match - but the Chelsea man himself has called on Aguero to apologise.
Luiz said: "Aguero is a great player but he needs to be honest with himself and say, 'I don't like to do bad tackles'.
"Kids see the game and they want to see the good things and not the bad - I would apologise. Football is beautiful, but sometimes in games people have five seconds like that - I forgive him because I have a good heart. I don't like to beat people.
"Sometimes in a game people have five seconds when they are angry and do things they don't like to do. I think it was that.
"I never saw Aguero do a bad tackle on other players."